BAGHDAD — Tens of thousands of Syrian Kurds swarmed across a bridge into neighboring Iraq’s northern self-ruled Kurdish region over the past few days in one of the biggest waves of refugees since the rebellion against President Bashar Assad began, U.N. officials said Monday.

The sudden exodus of around 30,000 Syrians amid the summer heat has created desperate conditions and left aid agencies and the regional government struggling to accommodate them, illustrating the huge strain the 2½-year-old Syrian conflict has put on neighboring countries.

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Thousands fleeing Syria enter Iraq at the Peshkhabour border point at Dahuk, 260 miles northwest of Baghdad. The Associated Press

The mostly Kurdish men, women and children who made the trek join some 1.9 million Syrians who already have found refuge abroad from Syria’s relentless carnage.

“This is an unprecedented influx of refugees, and the main concern is that so many of them are stuck out in the open at the border or in emergency reception areas with limited, if any, access to basic services,” said Alan Paul, emergency team leader for the Britain-based charity Save the Children.

“The refugee response in Iraq is already thinly stretched, and close to half of the refugees are children who have experienced things no child should,” he said, adding that thousands of refugees were stranded at the border, waiting to be registered.

The U.N. said the reason for this flow, which began five days ago and continued unabated Monday, is unclear. But Kurdish areas in northeastern Syria have been engulfed by fighting in recent months between Kurdish militias and Islamic extremist rebel factions with links to al-Qaida. Dozens have been killed.

Following the assassination of a prominent Kurdish leader late last month, a powerful Kurdish militia said it was mobilizing to expel Islamic extremists.

On Monday, activists said fighters from al-Qaida-linked jihadi groups shelled areas in the predominantly Kurdish town of Ras al-Ayn with mortars and artillery, coinciding with clashes in the area between Kurdish gunmen and jihadi fighters.

“Syrian refugees are still pouring into Iraq’s northern Kurdish region in huge numbers, and most of them are women and children,” said Youssef Mahmoud, a spokesman for the U.N. refugee agency in Iraq’s Kurdish region.

“Today, some 3,000 Syrian refugees crossed the borders, and that has brought the number to around 30,000 refugees since Thursday.” The latest wave has brought the overall number of Syrian refugees in the Kurdish region to around 195,000, he added.

The U.N. High Commissioner for Refugees has set up an emergency transit camp in Irbil, the capital of Iraq’s Kurdish autonomous region, to house some of the new arrivals. Some of the refugees were said to be staying in mosques or with family or friends who live in the area, according to the agency.

UNHCR said it is sending 15 truckloads of supplies from its regional stockpile in Jordan. It said the shipment should arrive by the end of the week.

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